Fault tolerance of hypercubes and folded hypercubes |
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Authors: | Litao Guo Xiaofeng Guo |
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Affiliation: | 1. Department of Mathematics, Xiamen University of Technology, Xiamen?, 361024, Fujian, People’s Republic of China 2. School of Mathematical Sciences, Xiamen University, Xiamen?, 361005, Fujian, People’s Republic of China
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Abstract: | Let \(G = (V,E)\) be a connected graph. The conditional edge connectivity \(\lambda _\delta ^k(G)\) is the cardinality of the minimum edge cuts, if any, whose deletion disconnects \(G\) and each component of \(G - F\) has \(\delta \ge k\) . We assume that \(F \subseteq E\) is an edge set, \(F\) is called edge extra-cut, if \(G - F\) is not connected and each component of \(G - F\) has more than \(k\) vertices. The edge extraconnectivity \(\lambda _\mathrm{e}^k(G)\) is the cardinality of the minimum edge extra-cuts. In this paper, we study the conditional edge connectivity and edge extraconnectivity of hypercubes and folded hypercubes. |
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